After successful completion of the course, students are able to

• recognize the most important basic types of partial differential equations,
• apply approaches and the necessary mathematical foundations to solve PDEs,
• classify second order linear partial differential equations,
• to calculate generalized and fundamental solutions and thus to solve boundary and initial value problems,
• examine the existence of solutions and
• present their solutions in front of peers.

Quasilinear first order equations. Linear elliptic, parabolic, and hyperbolic equations of second order. Methods: maximum principle, Sobolev spaces, variational principles, spectral analysis

Lectures, exercies and a revision course are being offered. In the lecture there will be an introduction to theory and examples will be calculated. Once a week, exercise-sheets will be calculated on the blackboard by the students.The repetition offers the possibliy to make questions relating the lecture. The repetition is a complementary and optional offer.

In the WS2020 the lectures are provided by Prof. Jüngel as videos in TUWEL. Questions can be posed in the weekly Q&A hour ("repetitorium"). The latter takes place via zoom.

The exercises take place via Zoom; the links to join the respective meetings can be found on TUWEL.

This courses is blocked until Christmas.

An introduction to the organisation of the course is given on Friday 01 October 2021 from 9:30-10:15am. The Zoom link is

https://tuwien.zoom.us/j/92880115946?pwd=NnpPaWdtYU1KNEIvSVlybVJZQXhCdz09

Meeting-ID: 928 8011 5946
Passwort: Winter2021

2 written tests + exercises (on blackboard) +1 oral exam

Lecture Notes available on the website: http://www.asc.tuwien.ac.at/~juengel->Teaching   (latest version: Nov. 2021)

* for the individual chapters of the course:
§1: Strauss §1.1-1.5; Evans §2.1
§2: Evans §3.2; Strauss §1.6, (14.1)
§3: Renardy-Rogers §5.1-5.3; Strauss §12.1
§4: Evans §2.2; Strauss §6.1-6.3, 7.3, 12.2
§5: Evans §5+6
§6: Straus §12.3, 2.4, 4.1; Evans §2.3.1, 2.3.3, 4.3.1, D.6, (7.1)
§7: Straus §2.1-2.2, 2.5, 3.2, 4.1, 9.1; Evans §2.4.1a, 2.4.3, 7.2

* general:
W.A. Strauss: Partial Differential Equations - An Introduction, John Wiley & Sons, 1992
L.C. Evans: Partial Differential Equations, AMS, 1998
F. John, Partial Differential Equations, Springer, New York, 1975.
M. Renardy, R.C. Rogers, An Introduction to Partial Differential Equations, Springer, New York, 1993
M.E. Taylor, Partial Differential Equations - Basic Theory, Springer, 1996

* analysis 1-3
* differential equations 1 (solving equations of 1st and 2nd order with constant coefficients [also inhomogeneous], variation of constants, separation of variables)
* functional analysis (in particular compactness, strong/weak convergence, L^p spaces, Hilbert spaces, dual spaces, Riesz-Fischer representation theorem, linear operators, spectrum)

It is recommended to take the exams for the above mentioned lectures before attending the lecture Partial Differential equations.